Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2017-6pp.708-714

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Total articles in the database: 10864
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L.D. Akulenko, V.G. Baidulov, D.V. Georgievskii, and S.V. Nesterov, "Evolution of Natural Frequencies of Longitudinal Vibrations of a Bar as Its Cross-Section Defect Increases," Mech. Solids. 52 (6), 708-714 (2017)
Year 2017 Volume 52 Number 6 Pages 708-714
DOI 10.3103/S0025654417060103
Title Evolution of Natural Frequencies of Longitudinal Vibrations of a Bar as Its Cross-Section Defect Increases
Author(s) L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5 str. 1, Moscow, 105005 Russia)
V.G. Baidulov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5 str. 1, Moscow, 105005 Russia, baydulov@gmail.com)
D.V. Georgievskii (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Lomonosov Moscow State University, Moscow, 119992 Russia)
S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia)
Abstract We study the evolution of characteristics of natural longitudinal vibrations of a circular bar in the case of increasing defect in its cross-section. It is shown that, in the limit case where the defect separates the bar into two independent fragments, the natural frequencies of the initially defect-free bar pass into the natural frequencies of its separate parts. The respective evolution of the natural modes of vibrations is observed. The evolution predicted by the theoretical analysis can be observed experimentally by using the resonance method and constantly increasing the defect till the final separation of the bar into two parts.
Keywords bar, cross-section defect, vibration characteristic evolution, natural frequencies
References
1.  V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in Theory of Vibrations (Nauka, Moscow, 1988) [in Russian].
2.  L. D. Akulenko and S. V. Nesterov, "Investigation of the Influence of Defects on the Natural Frequency Spectrum and Vibration Shapes of Rods," Vestnik Nizhegorod. Univ im. N.I. Lobachevskogo, No. 4(2), 32-33 (2011).
3.  L. D. Akulenko and S. V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications (CRC Press Co., Boca Raton, 2005).
4.  I. A. Krasnobaev, E. N. Potapenko, and E. N. Shcherbak, "Determination of the Beam Inhomogeneity Parameters from Resonance Frequencies of Its Longitudinal Oscillations," Izv. RGSU, No. 2, 67-73 (1998).
5.  V. A. Postnov, "Damage Identification in Elastic Systems by Mathematical Treatment of Experimentally Obtained Frequency Spectra," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 155-160 (2000) [Mech. Solids (Engl. Transl.) 35 (6), 129-133 (2000)].
6.  E. I. Shifrin and R. Ruotolo, "Frequencies of a Beam with an Arbitrary Number of Cracks," J. Sound. Vibr. 222 (3), 409-423 (1999).
7.  A. Colonnelo and A. Morassi, "Hearing Cracks in a Vibrating Rod," in Proc. ISMA 23, Vol. 3 (Leuven, 1998), pp. 1357-1363.
8.  R. Ruotolo and C. Surace, "Damage Assessment of Multiple Cracked Beams: Numerical Results and Experimental Validation," J. Sound Vibr. 206 (3), 567-588 (1997).
9.  J. Neumann, Introduction to Probability Theory and Mathematical Statistics (Nauka, Moscow, 1968) [in Russian].
10.  R. N. Iyengar, "First Passage Probability during Random Vibrations," J. Sound Vibr. 31 (2), 185-193 (1973).
11.  L. D. Akulenko, "A Quasioptimal Algorithm for Detecting and Determining Maneuver Parameters of a Dynamic Object," Izv. Ross. Akad. Nauk. Teor. Sist. Upravl., No. 2, 47-52 (2002) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 41 (2), 207-212 (2002)].
12.  V. A. Fok, "Theoretical Studies of Conductivity of a Circular Hole in the Partition across a Tube," Dokl. Akad. Nauk SSSR 31 (9), 875-878 (1941).
13.  S. V. Nesterov, "Experimental Studies of Conductivity of a Circular Hole in the Partition across a Tube," Dokl. Akad. Nauk SSSR 31 (9), 879-882 (1941).
Received 28 July 2017
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